Board of Governors of the Federal Reserve System
International Finance Discussion Papers
Number 1058, November 2012 --- Screen Reader
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Crisis and Calm: Demand for U.S. Currency at Home and Abroad from the Fall of the Berlin Wall to 20111

Ruth Judson

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Abstract:

U.S. currency has long been a desirable store of value and medium of exchange in times and
places where local currency or bank deposits are inferior in one or more respects. Indeed, as
noted in earlier work, a substantial share of U.S. currency circulates outside the United States.
Although precise measurements of stocks and flows of U.S. currency outside the United States
are not available, a variety of data sources and methods have been developed to provide
estimates.
This paper reviews the raw data available for measuring international banknote flows and
presents updates on indirect methods of estimating the stock of currency held abroad: the
seasonal method and the biometric method. These methods require some adjustments, but they
continue to indicate that a large share of U.S. currency is held abroad, especially in the $100
denomination. In addition to these existing indirect methods, I develop a framework and basic
variants of a new method to estimate the share of U.S. currency held abroad.
Although the methods and estimates are disparate, they provide support for several hypotheses
regarding cross-border dollar stocks and flows. First, once a country or region begins using
dollars, subsequent crises result in additional inflows: the dominant sources of international
demand over the past decade and a half are the countries and regions that were known to be
heavy dollar users in the early to mid-1990s. Second, economic stabilization and modernization
appear to result in reversal of these inflows. Specifically, demand for U.S. currency was
extremely strong through the 1990s, a period of turmoil for the former Soviet Union and for
Argentina, two of the largest overseas users of U.S. currency. Demand eased in the early 2000s
as conditions gradually stabilized and as financial institutions developed. However, this trend
reversed sharply with the onset of the financial crisis in late 2008 and has continued since then.

Keywords: Currency, banknotes, dollarization, crisis

JEL classification: C82, E4, E49

Unlike the banknotes of most other countries, the U.S. dollar is
used far beyond its borders as a medium of exchange and store of
value. This international aspect of dollar usage has important
implications for a wide range of Federal Reserve operational
considerations, including its currency production, processing, and
planning, the interpretation of currency figures as part of
monetary analysis, daily open market operations, management of the
Federal Reserve's portfolio, and analysis and forecasting of the
Federal Reserve's income.2 In addition, currency exports, like
other exports, figure in the U.S. balance of payments and
international investment position. Unfortunately, however, direct
measurements of the stocks and flows of U.S. currency outside U.S.
borders are not available, and a variety of indirect measurements
and proxies must instead be used. From these sources, though, a
fairly consistent picture emerges.

Despite the disparate methods and data sources, the data
consistently indicate several trends. First, international demand
for U.S. currency increased steadily over the 1990s and into the
early 2000s, a period that coincided with the fall of the Berlin
Wall, the collapse of the Soviet Union, and periodic economic and
political crises in several Latin American countries. Second,
international demand for dollars began to stabilize or decline
around the time of the introduction of the cash euro in
2002.3 This decline coincided with economic
and political stabilization and financial modernization in many
economies in and around the euro zone and the former Soviet Union
and continued until late 2008, when the global financial crisis
appeared to spark renewed demand for U.S. banknotes that has shown
no sign of abating.

In this paper, I present estimates of the stocks and flows of
U.S. currency abroad from the early 1990s through the end of 2011.
Section 1 reviews the available data sources, with a focus on their
strengths and weaknesses for use in answering questions about the
shares of banknotes held in the United States and abroad. Section 2
presents an overview of currency demand over the past several
decades and some stylized facts about the composition of U.S.
currency levels and changes over time. Section 3 builds on these
stylized facts and presents simple and direct estimates of stocks
and flows of U.S. currency abroad. Section 4 presents updates of
two indirect estimates of stocks and flows of U.S. currency held
abroad; these estimates are based on the data sources from Section
1 as well as additional information. Section 5 presents estimates
of a very simple currency demand equation for the United States,
from which estimates of the impact of international demand on
currency growth can be derived. Section 6 summarizes these findings
and concludes with some general observations and directions for
further work.

I. Data: An Overview

I.A. Total Currency in
Circulation

I.A.2. Public Data

In general, the aggregate quantity of genuine currency in
circulation is relatively easy to measure: it is physical, and it
is produced, transported, and issued under very secure
conditions.4 Official currency statistics for the
United States are reported by the Treasury and Federal Reserve,
which collaborate to produce data on currency in circulation,
generally defined as Federal Reserve notes, Treasury currency, and
coin held outside of the vaults of the Federal Reserve and the
Treasury.5 Figures on total currency in
circulation are reported weekly on the Federal Reserve's H.4.1 and
H.6 Statistical Releases; the quarterly Treasury Bulletin
provides additional detail on denominations of banknotes and coin
in circulation.

I.A.2. Internal Data

The Federal Reserve's internal accounting and production
processes require close monitoring of currency production,
processing, and movements; as a result, more frequent and detailed
data are available internally for Federal Reserve notes, which
constitute the vast majority of currency in circulation ($1.03
trillion of the $1.08 trillion total as of the end of
2011).6 In particular, accounting data provide
daily updates by denomination on the quantity of Federal Reserve
notes outstanding (that is, carried on the books of each Federal
Reserve Bank), and in the custody of each Federal Reserve Bank. In
addition, processing data provide monthly totals of Federal Reserve
note movements between each Federal Reserve office and circulation
by denomination.7 As shown in section 3, these data and
simplifying assumptions about domestic and international movements
of banknotes can be exploited to obtain estimates of stocks and
flows of U.S. currency abroad.

I.B. Data on Cross-Border Flows of U.S.
Currency

Movements of currency across U.S. borders cannot be precisely
measured for several reasons. First, there is no legal requirement
or mechanism to monitor movements of $10,000 or less, and many
individuals cross U.S. borders each year.8 The net movements of
currency across U.S. borders through such nonbanking channels are
potentially significant. Indeed, as noted in U.S. Treasury (2006),
customs reporting for Mexico indicates substantial cash flows from
the United States to Mexico in the hands of tourists and migrants;
such flows, since they typically occur in amounts of less than
$10,000 and through nonbanking channels, are not captured in U.S.
data. Second, even when there is a legal requirement to report
currency flows, mechanisms are not always in place to capture the
data and reporters might not comply with requirements. Despite
these challenges, informative measurements do exist.

I.B.1. Federal Reserve Commercial Bank
Shipment Data

The Federal Reserve provides currency on demand to all account
holders, including those who provide banknotes to international
customers. Many of these institutions, including most of the
largest wholesale banknote dealers, report monthly, on a voluntary
and confidential basis, the value and ultimate source or
destination country of their receipts and payments of U.S.
currency. While not all banks that deal in the international
shipment of banknotes provide these reports, the banknote shipping
business is highly concentrated and this dataset currently captures
the vast majority of banknote shipments that cross U.S. borders
through commercial banking channels.

This dataset begins in the late 1980s and covers virtually every
country in the world. The quality of the data varies across time as
the set of reporting dealers has evolved; for all practical
purposes, the dataset begins in the early 1990s. For example,
consider a shipment bound for Russia via Germany. The immediate
source or destination of the shipment can be identified by the
location of the counterparty. Thus, for a nonreporting dealer, the
dataset would only indicate a shipment to Germany, but a reporting
dealer would provide the ultimate destination, Russia. Conversely,
consider a shipment from Cambodia back to the United States via
Hong Kong. Data from a nonreporting dealer would indicate an inflow
of dollars to the United States from Hong Kong, but data from
reporting dealer would indicate the ultimate source of shipment as
Cambodia. The level of detail in the reporting has generally
improved over time as more dealers have begun to report, but the
trend can reverse if, for example, a reporting banknote dealer
leaves the banknote business and other nonreporting dealers begin
providing banknote shipment services to the departing reporter's
customers.

Two additional shortcomings of this dataset are that it covers
only banknote flows to and from the United States, and that it only
covers flows through the banking system. First, the dataset does
not cover U.S. banknote flows among other countries, which can be
substantial, especially in areas where large volumes of
cross-border trade are conducted in cash.9 The absence of such
information complicates any estimation of regional or country-level
holdings outside the United States, but does not affect aggregate
measurements of commercial bank currency shipment flows into and
out of the United States. However, banknote flows through nonbank
channels can also be significant, and observations gathered in the
course of the joint U.S. Treasury - Federal Reserve International
Currency Awareness Program indicate that several countries receive
dollar inflows through nonbank channels such as tourists or migrant
workers but return the currency to the United States through
banking channels.10 As a result of these shortcomings
and complications, the country-level data must be interpreted with
care and with an understanding of the institutional arrangements in
place through time.

I.B.2. U.S. Customs Data

In principle, the most obvious direct source of information on
U.S. currency flows across U.S. borders should be the Currency and
Monetary Instrument Reports (CMIRs), which are compiled by the U.S.
Customs Service. Individuals and firms making almost any shipment
of more than $10,000 in cash across a U.S. border are required to
file CMIRs, so these reports should be quite comprehensive and
informative. However, as noted in Treasury (2006), CMIRs are
neither accurate nor thorough measures of large cash shipments
outside the banking sector due to three shortcomings: a generally
one-sided system for collecting data, the omission of some
potentially large volumes of currency flows, and the inability to
accurately reflect flows to international custodial holding sites
for U.S. currency. First, all individuals entering or leaving the
United States are required to complete a CMIR if they are carrying
more than $10,000 in currency or monetary instruments. In practice,
though, customs formalities, including a specific question about
currency and monetary instruments, are required for individuals
entering the United States, but not for individuals exiting the
United States.11 As a result, it seems plausible that
underreporting is more likely for outbound travels. Second, even if
all travelers were to report accurately, the CMIRs require no
reporting for sums below $10,000; in aggregate, these sums could be
considerable. As noted above, 151 million passengers arrived and
departed on international flights at U.S. airports and about 200
million border crossings occurred by land in 2009 (U.S. Census
2012). Third, the CMIRs do not account properly for shipments to
international custodial holding sites for U.S. currency. These
sites, known as Extended Custodial Inventories, or ECIs, are secure
locations outside the United States at which U.S. currency is held
in custody for the Federal Reserve Bank of New York. Shipments to
these sites are recorded in U.S. Customs data when they physically
exit the United States, even though they remain in the custody of
the Federal Reserve Bank of New York. Thus, for example, a shipment
to an ECI in Switzerland will be recorded as a shipment to
Switzerland on the day it occurs even though the currency is not in
circulation.12

In addition, CMIR reporting requires only information about the
immediate source or destination of currency flows, not the ultimate
source or destination like the commercial bank shipment data. For
example, if an institution ships currency to Russia via Germany,
the commercial bank shipment data from a reporting institution
would record the destination as Russia while the CMIR data would
report the destination as Germany. We therefore consider the
shipments data described above to be superior to the CMIR data, and
hence we do not use the CMIR data in this study.13

II. Stylized Facts about U.S. Currency in
Circulation

II.A Overall Currency Growth Has Been
Strong

The death of cash has often been predicted, and it would seem
that demand for currency would thus grow somewhat more slowly than
income. Despite a general increase in the variety of payment media
as well as increasing noncash means of payment, though, U.S.
currency in circulation has grown at an average rate of about 6 to
7 percent annually over the past few decades, one to two percentage
points more rapidly than U.S. nominal GDP.1415

II.B. Overall U.S. Currency Movements are
Dominated by $100s

In value terms, the driving force over this period has generally
been growth in the $100 denomination, as can be seen in Figures 1A
and 1B.16 Figure 1A presents annual end-year
data on U.S. currency in circulation by denomination from 1989 to
2011. At the end of 2011, U.S. currency in circulation totaled
about $1 trillion, of which nearly $800 billion, or just over three
quarters, was in the $100 denomination.17 Figure 1B presents
annual growth rates for the same items, on a
fourth-quarter-to-fourth-quarter basis. The overall growth of
currency, the solid black line, moves closely with, though
generally more slowly than, the growth of $100 notes, the dashed
purple line. The correlation of overall currency growth with $100s
over this period is over 0.9; correlations with the other
denominations are generally decreasing in the denomination. The
correlation for $1s is about 0.2.

II.C. Crises Are Reflected in Aggregate
U.S. Currency Data

Figure 1B begins to reveal some general patterns in overall
currency demand. In particular, currency growth was quite strong in
the early 1990s, which coincided with the fall of the Berlin Wall
and the collapse of the Soviet Union. After a brief lull in the
mid-1990s, currency growth picked up again in the late 1990s,
driven by crisis in Argentina in 1997 and then concern about Y2K in
1998 and 1999. Following a dip in currency demand in 2000, which
largely reflected the return early in 2000 of precautionary stocks
accumulated late in 1999, demand was boosted in the early 2000s by
the events of September 11, which, judging by outsized commercial
bank shipments, led to strong overseas demand for currency in the
short run and, in the longer run, the apparent accumulation of
precautionary stocks at home and abroad. Demand then slowed over
the mid- to late-2000s until the sharp reversal seen in late
2008.18

II.D. Canadian Patterns of Currency Demand
Are Likely Similar to U.S. Domestic Currency Demand

One might look to Canada for evidence of what U.S. currency
demand would look like without a foreign component. Canada has
similar income levels, payments technologies, holiday patterns, and
GDP growth rates to those in the United States, but little Canadian
currency is believed to circulate externally. Figures 2A and 2B
display Canadian currency in circulation by denomination in levels
and growth rates from 1989 to 2011. As can be seen in Figure 2A,
$100s are also prevalent in Canada, though less dramatically than
in the U.S., accounting for just over half of Canadian currency in
circulation at the end of 2011.19 Overall currency growth rates for
Canada are, not surprisingly, driven less strongly by $100s and
more strongly by $20s and $50s (not shown), the primary transaction
denominations in Canada. Over the full half-century, the simple
correlation between overall currency growth and growth by
denomination is 84% for $100s, 86% for $20s, and 75% for $50s. More
recently, however, the role of $100s has apparently declined,
possibly as electronic payments have become more common.
Correlations over this period are, respectively, 63%, 87%, and
70%.

II.E. U.S. and Canadian Currency Growth
Relative to Income Diverged Beginning in the 1980s

As noted earlier, U.S. currency growth has been strong even
relative to nominal GDP. Figures 3 and 4 display the ratios of
total currency to nominal GDP for the United States and Canada over
the past half-century. Ordinary theories of money demand would
predict that the ratio of income to currency, or velocity (the
inverse of the ratio shown here) should vary positively with
the opportunity cost of holding money. That is, in terms of these
charts, higher opportunity cost would be associated with
lower demand for currency relative to income. As cashless
payments become more common and, presumably, more cost-effective,
one might expect that, abstracting from movements in market
interest rates, demand for currency relative to income should
decline. Indeed, that pattern prevailed in the United States until
about 1985, and in Canada generally for the period. The upturn in
the U.S. ratio of currency to nominal GDP beginning in 1989 is thus
anomalous and is consistent with substantial and growing external
use of U.S. currency.

In the next section, I present a very simple estimate of
overseas demand for U.S. currency based on these patterns and the
assumption that patterns of domestic demand for currency are the
same in the United States and Canada. I then juxtapose these
estimates with direct measurements of cross-border currency
flows.

III. Simple Estimates of Stocks and Flows
of U.S. Currency Held Abroad

III.A Two Estimates Based on Money Demand
and Comparisons with Canada

III.A.1. A Very Simple Estimate

Taken together, the difference between the patterns seen for the
United States and for Canada in Figures 3 and 4 suggest a simple
estimate of the share of U.S. currency abroad. As noted above, and
as displayed in Figure 5, U.S. and Canadian nominal GDP growth
rates have been similar over this period. The observed U.S. ratio
of currency to nominal GDP is the sum of domestic and foreign
demand. If we assume that the Canadian ratio of currency to nominal
GDP is the same as its U.S. counterpart for domestic demand, then
the foreign share of U.S. demand can be estimated as follows.
Define

Replacing CURRGDPUSA_Dom with CURRGDPCanada in the equation
above, it is then possible to solve for CURRUSA_For / CURRUSA_Tot
as

III.A.1. A Simple Estimate

The approach above carries with it the assumption that Canadian
and U.S. domestic demand for currency are the same at the same
point in time. However, the level of Canadian per capita income,
while similar to that of the United States, has generally been a
bit lower. Thus, an alternative assumption would be that Canadian
and U.S. domestic demands for currency relative to income are the
same at the same levels of per capita income. In order to construct
an estimate of the share of U.S. currency abroad using this
assumption, we proceed as follows. First we regress the ratio of
Canadian currency to GDP on the log and level of Canadian per
capita GDP, denoted GDPC:

To be sure, this specification is a very simple reduced form based
on the chart shown; it effectively assumes a log-linear structure
for demand for currency as a function of income and assumes no
other factors. We then construct the estimated domestic share of
U.S currency for a given level of GDPC as

where XCanUS is the U.S.-Canadian dollar exchange rate. The simple
estimate is then constructed as before, replacing CURRGDPUSADom
with
rather than
CurrGPDCan in Equation 2 and rearranging to solve for CURRUSAFor /
CURRUSATot, which gives

These two estimates of U.S. currency abroad are displayed in
Figures 6A and 6B. The GDP-based estimates, the solid lines,
suggest that about half of all U.S. currency, and about 65 percent
of $100s, were held abroad as of the end of 2011, for a total value
of about $500 billion. Over the past two decades, these estimates
point to a sharp runup in external demand for U.S. currency
beginning in the late 1980s, a brief pop in 1999, a decline
beginning in 2003, and a resurgence in 2008, all patterns
consistent with the overall growth of U.S. currency.

III.B. Measurements of Cross-Border Flows of
U.S. Currency

We now turn to the information provided by direct measurements
of currency flows. Figures 7 through 11 display annual data on the
primary measurements of cross-border currency flows in dollars, the
international commercial bank shipment data described in Section
I.B.1. Beginning with Figure 7, the solid black line indicates net
commercial bank shipments and the dashed blue line indicates the
total change in currency in circulation each year.20
Focusing only on the solid black and blue dashed lines, several
features of the data stand out. First, reflecting the strong
influence that international demand has on overall U.S. currency
demand, the two series generally move in parallel, though the gap
widens in the early 2000s and narrows in the most recent years.
Second, the spike seen in total currency in circulation, the blue
dashed line, is absent in the shipment flows. This feature of the
data reflects the fact that a large share of the runup in holdings
of currency immediately prior to the century date change (that is,
in the final weeks of 1999) was held in commercial bank vaults and
was then returned to the Federal Reserve early in 2000. Thus, while
the currency was technically "in circulation" in the sense that
it was held outside the Federal Reserve, the bulk of it never went
to bank customers.21

While U.S. currency is used in, and is shipped to and from, many
countries, a few areas stand out because of their size and their
appetite for dollars in times of crisis. In Figure 8, the dashed
red line indicates net commercial bank shipments to the two leading
markets in this category, the former Soviet Union and Argentina.
For all but the first and last few years of the period shown, or
from about 1995 to 2008, these shipments more than fully accounted
for all net commercial bank shipments. This phenomenon might also
have been the case in the early part of the sample, but reporting
in that period was not as detailed. As a result, shipments recorded
with a destination of Europe might well have been sent to the
former Soviet Union. In the early 2000s, net shipments to these
markets declined as the financial conditions stabilized and as the
need to use cash for saving and transactions has faded. In the past
two years, though, global conditions as well as crisis and
political uncertainty in these regions appears to have coincided
with an upswing in demand for dollars.22

Figure 9 displays a proxy for commercial bank shipments based on
currency processing data, the solid gray line. Commercial bank
shipments are reported on a confidential basis, and monthly data
are not always available on a consistent schedule. In order to have
data for operational and publication purposes, Federal Reserve
Board staff developed this proxy, which is the sum of net payments
of $100 notes from three Federal Reserve offices known to handle
substantial volumes of deposits and withdrawals sent from or to
international destinations: New York, Los Angeles, and
Miami.23 This proxy is based on two
assumptions, which differ from the true net shipments series in two
offsetting ways. The first assumption, which likely results in an
overestimate, is that all payments and receipts at these offices
are to or from international counterparties and that all payments
and receipts at other offices are to or from domestic entities; in
fact, every Federal Reserve office serves domestic and
international customers. The second assumption, which would
generally result in an underestimate, is that only $100s are sent
to or received from international destinations. This proxy moved
very closely with the total shipments data in the 1990s, but was
considerably higher than shipments over most of the 2000s, perhaps
suggesting that domestic demand for $100s was stronger in that
period.

The two dashed series in Figure 9 indicate two experimental
series. As noted above, one shortcoming of the shipment dataset is
that it captures only cross-border flows carried through commercial
banking, or "wholesale" channels. However, as reported in U.S.
Treasury (2006), many countries receive large dollar flows through
nonbank, or "retail" channels and return dollars to the United
States through banking channels. In the commercial bank shipment
data, this phenomenon emerges in the form of persistent negative
net shipment figures. That is, the shipment figures indicate large
flows of dollars out of the foreign country into the United States
and much smaller flows in the opposite direction.

For some such countries, the net commercial bank shipments
figures are likely accurate and reflect dollar banknote inflows
from third countries. For example, if tourists from Country A
routinely carry dollars to Country B and the residents of Country B
have little other use for dollars, the dollars might be shipped
from Country B to the United States. All other factors equal, this
pattern would result in negative net shipments figures, and
shipments figures summed across Country A and Country B would give
an accurate indicate of flows into and out of the United States.
For some countries, however, it is likely that dollars arrived in
the country from the United States through nonbank channels. In
such cases, the commercial banknote flows would not give an
accurate indication of net flows to and from the United States.

The first experimental series imposes a very rough adjustment
for this phenomenon as follows. First, a group of countries known
to have significant tourism or significant populations of
immigrants or migrant workers in the United States is identified.
Second, a group of countries whose total net shipments is
substantial and negative is identified. Third, for each year and
for each country in both groups, the assumption is imposed that
total net currency shipments to these countries, including the
observed net commercial bank "wholesale" flows and nonbank
"retail" flows, were zero.

As with the shipments proxy, this approach embodies two
assumptions. First, this approach implicitly assigns a value of
zero for net currency flows to these countries. This assumption
could be erroneous in either direction: actual net flows could be
positive or negative. Second, this approach assumes that other
countries' flows in aggregate are accurately measured by net
commercial bank shipments. The blue dashed line shown here displays
an adjustment that imposes this assumption for about a dozen
countries. While this approach is admittedly crude, it is
suggestive of the magnitude of flows that could be occurring
through nonbank, or "retail" channels. Ideally, we could refine
this measure by constructing series of "retail" (nonbank channel)
banknote flows from the United States to other countries. While
this type of data is not available universally, it is collected by
some countries, including Mexico.24 This measure, the
dashed black line, also tracks the shipments proxy for most of the
sample, though it becomes implausibly large in the last few years
of the sample. To the extent that this adjustment it useful, it is
probably more applicable for cumulative, or stock estimates, than
it is for flow estimates, because the nonbank flows likely occur at
different times than the measured banking-channel flows back to the
United States. For example, currency might be brought from the
United States to another country through nonbanking channels over
time and then return quickly in the event of a regulatory or other
political or economic change.

Finally, the dashed gray line is an adjusted shipment proxy
series. Along the lines of the adjusted commercial bank series,
this series includes only payments of $100s from the Federal
Reserve Bank of New York, which are generally positive, and omits
payments from the Miami and Los Angeles cash offices, which are
generally negative and might reflect reflows of currency that moved
across U.S. borders through nonbank channels.

Figures 7 through 9 display nominal values, which can be
misleading even in a period with relatively low inflation. Figure
10, therefore, displays all of the same series as in Figures 7
through 9, but scaled by the stock of currency in circulation at
the end of the previous year, or the approximate percentage-point
contribution to currency growth that would be implied by each of
these measures. While the measures certainly vary, they generally
point to strong contributions from foreign demand in the early to
mid-1990s, a slowing in the mid-2000s, and a resurgence beginning
in 2008.

III.C. Using Cross-Border Flow Estimates to
Construct Estimates of the Stock of U.S. Currency Abroad

While tracking movements in currency in circulation is the major
object of operational interest, having an estimate of the stock of
U.S. currency abroad is also important for various analytical and
operational questions faced by the Federal Reserve. Figures 11A and
11B chart the stocks of currency in circulation implied by the flow
measures presented earlier. In Figure 11A, each line represents the
cumulative change in the item since the end of 1988, when currency
in circulation was about $230 billion. As indicated by the thicker
gray dashed line, total U.S. currency in circulation worldwide has
increased by just under $800 billion since 1990. The most direct
measurement, commercial bank shipments, the solid black line,
suggests that $200 billion has moved abroad since 1990, which would
put the total at between $200 billion and $400 billion, depending
on the assumed initial value. The shipments proxy, the solid gray
line, suggests that about $350 billion moved abroad over the
period, putting the total at $350 billion to $550 billion.25
Finally, the adjusted shipments and proxy figures, the dashed black
and gray lines respectively, suggest that about $550 billion moved
abroad over the period, putting the total at $550 billion to $750
billion. These ranges are, of course, large, though the simple
method proposed above in Section III.A.2 produces an estimate very
close to the center of the range.

Finally, Figure 11B displays the cumulative flow measurement and
estimates as a share of the cumulative increase in currency in
circulation at each point in time. Again, the estimates are
disparate, but indicate some common trends, including a strong role
for international demand in the 1990s, a waning role in the early
2000s, and a resurgence in 2008. In this Figure, as earlier, the
role of the former Soviet Union and Argentina is likely understated
because of poor data coverage in the shipment data in the early
1990s.

IV. Indirect Estimates of the Share of
U.S. Currency

Earlier work on estimates of the stock of currency abroad has
developed and provided estimates from two methods, known as the
seasonal method and the biometric method.26 Updates to these
methods continue to indicate that a substantial share of U.S.
currency is abroad, but technical factors and shifting patterns of
currency demand have made their use more challenging.

IV.A. The Seasonal Method

IV.A.1. Key Assumptions

The seasonal method extracts an estimate of the share of U.S.
currency abroad by working from four key assumptions. First, we
assume that the seasonal pattern in domestic demand for U.S.
dollars is similar to the seasonal pattern of demand within Canada
for Canadian dollars (similar holidays, vacations, customs, and
denominations). More specifically, we assume that the seasonal
amplitude, or the percentage difference between the seasonal peak
and seasonal trough, is similar for U.S. and Canadian currency
demand.27 Second, we assume that foreign
demand for U.S. dollars has no significant seasonal pattern, or,
correspondingly, that the seasonal amplitude for the foreign
component of demand for U.S. dollars is zero. Third, we assume that
circulation of Canadian dollars outside of Canada is negligible, so
that the demand for Canadian dollars can be attributed solely to
domestic demand. Finally, we assume that U.S. currency is not used
to a substantial degree inside Canada.

IV.A.2. Model

Based on these assumptions, we can express the seasonal model as
follows:

Define:

Sij = seasonal amplitude for country i, component
j

t = fraction of currency held abroad at
time t

The overall seasonal amplitude in U.S. currency, SUST,
can be expressed as a weighted sum of domestic (d) and foreign (f)
components:

(S1)

We cannot separately identify SfUS,t and SdUS,t
but, using the assumptions above, we replace SfUS,t with 0
and SdUS,t with STCan,t to obtain:

(S2)

Or, solving for t:

(S3)

IV.A.3. Application and Estimates

We estimate the share of all currency abroad and the share of
$100s abroad using X-12 ARIMA and an alternative shorter smoothing
window to obtain seasonal factors for U.S. and Canadian currency in
circulation. Once the seasonal factors are estimated, the seasonal
amplitude must be calculated.

In earlier estimates using this method, the peak month was
December and the trough month was February of the following year.
However, it seems that seasonal factor patterns have changed in the
past several years, as illustrated in Figures 12A and 12B. December
remains the clear peak, though its relative magnitude has varied
over time. In particular, February is no longer the trough for U.S.
currency in circulation. Rather, September is now the trough,
though January seems to track the lower envelope of September and
February. Moreover, January's seasonal factor is near the trough
for Canada as well.

Because of these shifts over time, I propose three approaches to
measuring the seasonal amplitude. For each, I report results using
two different seasonal adjustment procedures, X12-ARIMA and X12
with a shorter 3x1 smoothing window, shown in black and blue
respectively. The first approach estimates the annual amplitude as
the difference between the seasonal factor for December of one year
and January of the next year. These estimates are associated with
the year in which December falls and are shown in Figures 13A and
13B as the "annual" estimate, the solid lines. Second, one might
choose to fix the months used to calculate the U.S. seasonal
amplitude so that they are the same as the months used to calculate
the Canadian seasonal amplitude for a given observation. For these
"monthly fixed" estimates, shown as the dashed lines, the
Canadian seasonal amplitude for a given month is calculated as the
difference between the maximum and minimum seasonal factors
calculated for the most recent twelve months. The U.S. seasonal
amplitude for the same month is calculated as the difference
between the seasonal factors in the same months as for the Canadian
seasonal amplitude, and the monthly share of currency abroad is
then estimated as the trailing average of the estimates for the
past twelve months.28 A third approach is to estimate the
seasonal amplitude each month as the difference between the maximum
and minimum seasonal factors over the most recent twelve months,
and then to estimate the monthly share of currency abroad as the
trailing average of the estimates for the past twelve months. The
estimates from this approach are shown in Figures 13A and 13B as
the "monthly" short-dashed lines.

The results of the seasonal estimates for all currency abroad
and for $100s through December 2011 are displayed in Figures 13A
and 13B. As was the case in earlier work, these estimates are on
the high end of the range. These estimates also show a quite
different time series pattern relative to one another as well as
relative to other flow-based measures, though the monthly measures
generally indicate an upswing in the share of U.S. dollars held
abroad.

IV.B. The Biometric ("Fish")
Method

IV.B.1. Background: Use for Estimating
Wildlife Populations

The biometric method, also known as the "fish" method, applies
a method developed by Petersen (1893) to estimate fish populations
to cash processing data to obtain estimates of the "populations"
of notes in the United States and the rest of the world.29 In
the biological application, populations are estimated by capturing
some animals, tagging them, releasing them, and then recapturing
another sample of animals later. Assuming that both samples are
representative, the share of tagged animals in the general
population should be the same as the share of tagged animals in the
second sample, and the population can thus be estimated. More
formally, suppose M animals out of N total are captured and
tagged. Next, suppose that in the second sample, m tagged
animals are found out of n captured. Assuming that both
samples were representative, the share of tagged animals in the
second sample, m/n, should be equal to share of all tagged
animals, M, in the general population, N, or
m/n = M/N. Since M, m, and n are known, N can be
estimated as N=(n/m)*M.

IV.B.2. Application to Estimates of Banknote
Populations

We apply this method to banknotes by using monthly cash
processing data from Federal Reserve offices, changes in banknote
design, and background information about international banknote
shipping patterns. Specifically, we estimate the "population" of
notes in the rest of the world by estimating the "population" of
notes in the area served by the Federal Reserve Bank cash offices
in New York, Los Angeles, and Miami. Although banknotes are not
tagged, new designs are introduced from time to time, and
processing statistics distinguish between new-design and old-design
notes in some cases.

The Federal Reserve introduced new-design $100 notes in 1991 and
in 1996; a further redesign for the $100 note has been announced,
but the issuance date has not yet been announced.30 From
the moment each new design was issued, all new banknotes paid out
were of the new design. These notes were defined as the "marked"
or "tagged" notes. Following the analogy to the biologists'
technique, the second sample of notes occurs when notes are
returned to the Federal Reserve for processing. Notes returned to
Federal Reserve Bank cash offices are authenticated and evaluated
for fitness for further use; data on these processing operations
are kept by series.31 We focus on $100 notes here because
they are the most significant in dollar value and in the
international market.

The assumption that the "marked", or new-series, notes are
just as likely to be returned to Federal Reserve offices as
older-series notes is quite strong. It is likely more accurate for
the 1990-series notes than for the 1996-series notes because the
1996 series was a much more obvious design change: to the extent
that dollar users might prefer one series to another, that
preference might be stronger for the series with a more significant
design change. As with other assumptions, though, the sources of
error for this assumption could affect the estimates in either
direction: older notes might be underrepresented in Federal Reserve
receipts if they are hoarded, or out of active circulation, or they
might be overrepresented if dollar users prefer to retain newer
notes.32 Much more detailed processing data
would be needed to analyze these questions.

IV.B.3. Adjustments and Updates

These estimates provide an update as well as some adjustments to
previous estimates. The updates currently extend through the end of
2011. The adjustments are the result of corrections to anomalies in
the processing data detected in the process of calculating the
updates. In particular, recall that a key variable is the share of
"tagged", or new-series notes in notes received at Federal
Reserve Bank offices. In reviewing the data, we noticed that the
processing data for some offices and months implied shares that
were anomalous: The values were zero, one, or far away from either
values in adjacent months or from values reported by other offices
for the same month.

We adjusted the data by identifying anomalous observations and
assigning estimated share values. For all offices, a value of zero
or one was defined as anomalous. For all but two Federal Reserve
Bank cash offices, an office's monthly figure on the share of
new-series notes processed was defined as anomalous if the figure
was more than one standard deviation above or below the mean
processing share reported by all offices for that month. For the
remaining two Federal Reserve Bank cash offices, Miami and Los
Angeles, observations were defined as anomalous if they were more
than three standard deviations above or below the mean processing
share for the month. For all offices, the estimated share was
assigned the previous month's value for that office.

After these corrections, we estimated the "population" of
notes in two "pools", domestic and foreign. The foreign "pool"
includes either the New York and Los Angeles offices or the New
York, Los Angeles, and Miami cash offices; the domestic "pool"
includes all other offices.33 In addition, we produce two sets of
estimates for the share of notes held abroad, one using the actual
total quantity of notes in circulation, which is known, and one
using the estimated total quantity of notes in circulation. By
necessity, these estimates are calculated separately for
1990-series and 1996-series notes. Figure 14 displays the estimated
share of $100s in circulation abroad for 1990-series notes, the red
dashed line, for 1996-series notes, the blue long-dashed line, and
for both types of notes, the solid black line, based on the
estimated total stock of notes and based on the assumption that the
foreign "pool" is the New York and Los Angeles offices. The
estimates using the actual (known) total stock of notes are similar
and converge over time, suggesting that the biometric method is
better able to estimate the true total quantity of notes in
circulation only after the design has been in circulation for a few
years. Indeed, as shown in Figure 14A, the biometric method's
estimates of total notes in circulation converge to actual figures
and remain close.

Because of the timing of the introduction of the series of
notes, it is difficult to assess the trend in the share of $100s
abroad in the late 1990s, but both sets of estimates show a general
decline in the share of $100s abroad beginning in the late 1990s,
from somewhere between 65 and 72 percent to a bit under 58 percent
by about 2007. As in the flow data, the biometric method indicates
a sharp turnaround in late 2008; this method now indicates that
about 62 percent of $100 notes were in circulation abroad at the
end of 2011. Estimates using the New York, Los Angeles, and Miami
offices as the foreign pool are about 5 to 10 percentage points
lower; however, as with the shipment flows discussed earlier, it is
difficult to know how to interpret consistently negative inflow
data.

Estimates using this method for $50 notes indicate similar
patterns over time with somewhat lower shares abroad--about 40
percent at the end of 2011. When combined with the estimates for
$100s, these estimates suggest that about $510 billion, or just
over half of all U.S. currency in circulation was held abroad at
the end of 2011: about $480 of the $780 billion in $100s and about
$30 billion of the $70 billion in $50s in circulation.

V. Estimating a Currency Demand
Function

Finally, we return to the idea of a currency demand function,
which was briefly explored in Section 3 with reference to Canada.
Here, the approach is to specify a demand function for U.S.
currency that allows for foreign shipments as well as domestic
factors. Our general assumption has been that currency demand
consists of two components: a domestic component, which should be
correlated with the typical determinants of money demand; and an
international component, which is driven by routine as well as
crisis-related fluctuations in foreign demand for U.S.
currency.

Table 1 presents coefficient estimates for a simple error
correction model for the currency component of M2 estimated
quarterly beginning in 1988, a date chosen for two reasons.34
First, 1988 marks the beginning of availability of the commercial
bank shipment data as well as an apparent upshift in international
demand for U.S. currency. Second, preliminary testing (not shown)
indicates a distinct structural break in 1988. The regression model
consists of two equations, one for the steady state and one for
dynamics.

SHIP: Two-month moving average of commercial bank shipments
adjusted for negative net shipments, divided by the previous
period's seasonally adjusted currency component of M2. This
formulation puts shipments on the same basis as the monetary
aggregate growth data, which are calculated as monthly
averages.

Rshort: Short-term interest rate, a proxy for the opportunity
cost of holding currency

Trend: 1 for 1988:Q1 and increasing by 1 each quarter

Y2K: Dummy: 1 for 1999:Q4 and -1 for 2000:Q1

The coefficients in the steady state equation are constrained to
unitary elasticity, and the coefficients on the lagged values of
log changes in currency and GDP are constrained to sum to 1. The
equations are estimated by nonlinear least squares in one step by
substituting for the error term in the dynamic equation. After
controlling for the estimated contribution of overseas demand, the
coefficients are generally of the expected sign and magnitude. The
short interest rate is positively correlated with velocity, the
error correction coefficient is negative, shipments are strongly
significant, and recent lags of currency growth and income are
significant. The time trend coefficient is somewhat
counterintuitive, but its overall contribution is small and so we
leave further examination of it for future work.

Figure 15A displays overall currency growth, the solid black
line, the proxy measurement, the short-dashed red line, and nominal
GDP growth, the dashed gray line, for the regression sample period.
Finally, Figures 15B and 15C display the quarterly and cumulative
contributions to currency growth from foreign demand implied by the
regression in Table 1. In both figures, the contributions are
calculated from dynamic forecasts with residuals applied equally to
the two components. As indicated by the dashed red line in Figure
15C, international shipments, as measured by the $100s proxy, are
responsible for about two thirds of the growth in currency over
this period.

Notably, even the highest of these estimates suggests that
currency holdings by U.S. residents are significant--at least
$1,000 per person--a finding at odds with survey work on currency
holdings.35 Feige (1996, 2012) suggests that
underground economic activity could account for this discrepancy,
though underreporting, especially by individuals with large cash
holdings, is also likely a substantial problem.

VI. Summary, Conclusions, and Directions
for Future Work

In sum, much as in earlier work, the currently available data do
not allow for precise estimates of foreign holdings of U.S.
currency, and the available estimates are somewhat disparate.
Nonetheless, direct measurements, regression-based estimates, and
indirect estimates all point to strong international demand in the
1990s, a falloff in the early 2000s, and a recent resurgence that
coincided with the collapse of Lehman Brothers.36 Collectively,
these methods suggest that half or a bit more than half of U.S.
currency circulates abroad.

There are many promising avenues for future investigation,
including the following. For the biometric method, what might we be
able to learn about hoarding of notes? Will biometric estimates
change when the new $100 note is issued? For the seasonal method,
what is the significance, if any, of the shift observed in seasonal
patterns of demand for U.S. currency? For the regression-based
methods, would a more rigorous and sophisticated regression
framework yield more precise or very different estimates? Finally,
are there quantifiable indicators of market tension that show a
systematic relationship with external demand for U.S. dollars, and
can any of those indicators be forecasted? Some work along these
lines shows promise, but is in the early stages.37

Appendix: Currency Data Sources and Definitions

Several agencies and publications carry data on U.S. currency in
circulation, and several additional sources are available
internally in the Federal Reserve. The publications and the level
of detail provided by each source are summarized in table 1. None
of these sources provides any information about domestic and
international movements of U.S. currency.

NotesCurrency in circulation includes Federal Reserve notes,
Treasury notes, no longer issued notes, and coin held outside the
Federal Reserve and Treasury.Federal Reserve notes, net includes Federal Reserve notes
outstanding less Federal Reserve notes held at the Federal
Reserve.The currency component of the money stock includes currency
(including coin) outside the U.S. Treasury, Federal Reserve Banks,
and the vaults of depository institutions.

Porter, Richard D. (1993), "Estimates of Foreign Holdings of
U.S. Currency--An Approach Based on Relative Cross-Country Seasonal
Variations," in Nominal Income Targeting with the Monetary Base
as Instrument: An Evaluation of McCallum's Rule, Finance and
Economics Discussion Series Working Study 1 (Board of Governors of
the Federal Reserve System, March).

------, and Ruth A. Judson (1996), "The Location of U.S.
Currency: How Much is Abroad?" Federal Reserve Bulletin,
vol. 82 (October), pp. 883-903.

U.S. Census Bureau (2011), Statistical Abstract of the United
States 2012. Washington DC: U.S. Government Printing
Office.

U.S. Treasury (2006). The Use and Counterfeiting of U.S.
Currency Abroad, Part III. Washington DC: U.S. Department of
the Treasury.

Footnotes

1. Valentin Bolotnyy did a superb job of
updating and organizing many of the estimates presented here, and
his work was instrumental in the corrections to the biometric
method reviewed in section 3. In addition, this work would have
been impossible without the generous assistance of, and
thought-provoking discussions with, Dick Porter (FRB-Chicago);
Joann Freddo, Eileen Goodman, Jeff Pruiksma, Elliot Shuke, and
Charles Sims (FRB-New York); Carol Bertaut, Neil Ericsson, Jaime
Marquez, John Roberts, Charlie Thomas, Shaun Ferrari, Michael
Lambert, and Lorelei Pagano (Board of Governors); and Ed Feige. All
errors and omissions are mine. Return to
text

2.
Until late 2008, Federal Reserve notes, the dominant form of
currency, were the primary liability on the Federal Reserve's
balance sheet. As a result, currency demand was thus a primary
consideration in the conduct of daily open market operations as
well as in longer-range planning related to the Federal Reserve's
System Open Market Account portfolio. After late 2008, deposits of
depository institutions (of which reserve balances are the vast
majority) increased significantly and now exceed currency as a
liability on the Federal Reserve's balance sheet. Appendix Figure 3
illustrates the major components of the Federal Reserve's balance
sheet since 2003. Return to text

3.
The euro currency was introduced as a unit of account in 1999; the
physical currency was introduced in 2002. Return to text

4.
The quantity of counterfeit currency in circulation at any point is
not known, but estimates suggest that circulating counterfeits are
extremely small relative to genuine currency, on the order of one
to three in 10, 000 (Judson and Porter (2010)). Return to text

5.
Appendix table 1 provides a list of sources of currency data along
with a description of the different definitions of
currency. Return to text

7.
The locations and boundaries of the twelve Federal Reserve
districts were set when the Federal Reserve was established in
1913. Within each district, cash processing occurs at one or more
cash offices. The number and location of these offices varies over
time. Processing data are reported separately for each
office. Return to text

8.
In 2009, 151 million passengers arrived and departed on
international flights at U.S. airports and about 200 million
border crossings occurred by land (U.S. Census 2012). Return to text

10. This phenomenon is addressed in more
detail in the discussion of the flow data. Return to text

11. Passengers on flights departing the
United States are sometimes questioned or informed about this
reporting requirement, but coverage is far from complete.
Return to text

12. Refer to U.S. Treasury (2006), Chapter
5, for more details about ECIs. Return
to text

13. For researchers who do not have access
to the shipment data, or for certain countries and time periods,
the CMIR data can provide useful insights. Refer, for example, to
Feige (1996, 2012) for analysis of the U.S. economy and to Kamin
and Ericsson (2003) for analysis of dollarization in Argentina. For
the latter analysis, CMIR data were both available over a longer
time period and more reliable than usual because of the patterns of
dollar flows to Argentina. Return to
text

16. In piece terms, however, U.S. currency
is dominated by smaller denominations. As of late 2011, $1s were
32% of notes in circulation, $2s to $10s were 16%, and $100s were
25%. Appendix Figures 1A and 1B provide a breakdown of U.S. and
Canadian currency by denomination in value and piece
terms. Return to text

17. These figures are from the Treasury
Bulletin: http://www.fms.treas.gov/bulletin/b2011_1.pdf.
Return to text

18. Hellerstein and Ryan (2011) find
systematic relationships between currency shipments and inflation
and other factors. Return to
text

19. Both the United States and Canada have
notes of denominations above $100 in circulation, but in both
cases, these notes have not been issued to circulation for some
time. Return to text

20. Net commercial bank shipments are
defined as shipments out of the United States to other countries
(exports) less shipments from other countries into the United
States (imports). Return to text

21. For many internal calculations, we
typically smooth through this spike because of its extremely
transitory and peculiar nature. The currency component of the money
stock excludes currency held in the vaults of depository
institutions. We would ordinarily prefer to use this currency
component measurement, but data are not available by denomination
on that basis. Return to text

22. Work on disentangling the relative
importance of internal and external economic and political crisis
for currency demand in these countries is currently
underway. Return to text

23. The Federal Reserve System has 12
regional Banks, whose locations are fixed. Many Federal Reserve
Banks also have one or more branches, whose number and location can
change over time as operational needs dictate. The Miami office is
a branch of the Federal Reserve Bank of Atlanta and the Los Angeles
office is a branch of the Federal Reserve Bank of San
Francisco. Return to text

24. Mexico is the largest single
contributor to this adjustment, and it was the case of Mexico that
inspired this approach. In the 1990s, Mexico collected customs data
on cash imports from all travelers with no lower bound on the
reporting threshold. This reporting is, of course, subject to the
same problems of underreporting as other customs data, but the
magnitudes were substantial and of a magnitude similar to reported
commercial bank inflows. More recent customs reporting requires
only declaration of amounts above $10,000. Regardless, Mexican
statistics on tourism flows indicate substantial volumes of people
and revenue, though the form of the revenue (cash, credit card, or
other) is not specified. Refer to Banco de Mexico (2012).
Return to text

25. The proxy is the only measurement
available before 1988. It indicates that $40 billion moved abroad
over the period from 1974 to 1989; during that time, currency in
circulation increased by about $180 billion. Return to text

27. Of course, Canadian and U.S. holidays
are not identical: to give just two examples, Canada observes
Thanksgiving in October and the U.S. observes it in November, and
Canada's holidays include the day after Easter and the day after
Christmas while these days are not generally holidays in the United
States. Nonetheless, the broad outlines of holidays are very
similar, especially at a monthly frequency. Return to text

28. In the last two methods, one could
just as easily use the unsmoothed seasonal amplitude estimates.
These estimates, though, show a step-function-like shape because
the seasonal maximums and minimums generally change once per year.
It seems unlikely that the share of currency abroad follows such a
step function, and so the moving average imposes a smooth trend.
Notably, this averaging does not affect the level of the share
estimates on average over time. Return
to text

29. LeCren (1965) notes that Petersen did
not use the method for counting but that others properly credit him
with the method. Return to text

30. For more information on the earlier
changes to U.S. banknote design, refer to Allison and Pianalto
(1997). Return to text

31. For operational reasons, it is
important for Federal Reserve analysts to be able to assess the
longevity and other features of notes by their design or
series. Return to text

32. The 1990-series notes incorporated
microprinting and a security thread but retained the same portrait
and the same size and location for the portrait. The 1996-series
design changes included a larger portrait moved off the center of
the note. Return to text

33. In the original formulation of this
estimate, the foreign pool included only New York and Los Angeles.
Subsequent large volumes of activity attributable to international
demand prompted the addition of the Miami office to this group. The
estimate based on just the New York and Los Angeles offices is
analogous to the adjustment commercial bank shipments estimate: it
assumes that receipts at the Miami office reflect unmeasured
outflows and assigns a net value of zero. Return to text

34. As noted in Section III.B., the
currency component of M2 excludes currency held in the vaults of
depository institutions, or vault cash, which was one of the most
volatile components of currency in circulation just before and
after the century date change. Thus, this measurement of currency
is more useful for longer-term analysis where the inclusion of the
large and transitory swings in vault cash might be inordinately
influential, such as in quarterly measurements where the periods
immediately before and immediately after the century date change
fall into different quarters. Return to
text

35. The most recent Survey of Consumer
Payment Choice, conducted in 2009, indicates holdings of less than
$100 per person (Foster et al., 2011). Return to text

36. Indeed, weekly data, reported in
Appendix Figure 2, show an unmistakable turnaround in demand
patterns in the middle of September 2008. Return to text

37. Thus far, analysis along these lines
has appeared only in internal Federal Reserve
documents. Return to text